Greek campaigners seeking the return of the Parthenon marbles have renewed their efforts with an open letter imploring David Cameron to back the restitution of the classical carvings "to their historic home in Athens".

Stephen Fry is lending his support for the return of what are also known as the Elgin marbles.

Weighing in to one of the world's most controversial cultural disputes, the actor proposed that Britain "redress a great wrong" by using the occasion of the 2012 London Olympics to give up the fifth-century BC masterpieces. Nearly 200 years after the sculptures were acquired by the British Museum their return would not only be "classy", he argued, but a much-needed morale booster for a country mired in crisis.

"Stephen Fry knows more about this issue than most Greeks," said Alexis Mantheakis, who chairs the International Parthenon Sculptures Action Committee. "He makes the superb point that the London Olympics would be a perfect opportunity for Britain to magnanimously put an end to what Greeks and the majority of people in the EU, including the UK, see as a historical wrongdoing."

In the letter, the campaigning group cites a lengthy essay, Greece is the Word, that Fry recently penned on the issue.

"The Hellenic republic today is in heart-rending turmoil, a humiliating sovereign debt crisis has brought Greece to the brink of absolute ruin. This proud, beautiful nation for which Byron laid down his life is in a condition much like the one for which he mourned when they [the Greeks] were under the Ottoman yoke in the early 19th century," the actor wrote.

In its darkest hour, he said, Greece was now "owed" by Britain.

"What greater gesture could be made to Greece in its appalling finance distress? An act of friendship, atonement and an expression of faith in the future of the cradle of democracy would be so, well just so damned classy."

Global advocates of the antiquities' repatriation have pledged to step up pressure on the British government ahead of the July 27 opening of the Olympic Games.

In Sydney at the weekend, activists launched a new push to reinvigorate the campaign. Committees from around the world, including Australia and the US, announced they will meet in London in June to decide how best to promote the "noble cause."

Designed by Pericles's master sculptor, Phidias, the marbles were part of a monumental frieze that adorned the Parthenon. In 1801, they were removed from the Acropolis by Lord Elgin, then British ambassador to the Ottoman empire.

More than 60% of the frieze is now on display in Bloomsbury, while an ultra-modern museum, custom-built to exhibit the artworks at the foot of the Acropolis, has had to make do with giant plaster-cast copies.

With the Greek government noticeably abstaining from the dispute in recent years – with officials invariably citing Athens's dire financial straits – citizens exploiting social media have stepped into the breach. Mantheakis's own group has attracted 215,000 members worldwide since its foundation in 2009.

"Prime minister, history and future generations will honour you, as will Greece, if you take that one small but monumental step of amending the 1933 Museums Act to allow for the return of the Parthenon sculptures," said his open letter.

"If Britain could give back India, then surely the emptying of one room of a London museum is a small price to pay to right a historical wrong."

• This article was amended on 3 and 4 April 2012. The original headline referred to the Elgin Marbles. This has been corrected in accordance with the Guardian style guide. A reference to the fifth-century marbles has been clarified.